Topological Censorship
Montag, 4.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
FORMULATING CAPILLARY SURFACES IN THE CONTEXT OF VARIFOLDS
Dienstag, 5.12.23, 16:00-17:00, Raum 125, Ernst-Zermelo-Str. 1
Capillary surface is a fundamental geometric object, describing a particular boundary behavior of surface in a given container. In some recent works of Kagaya-Tonegawa (Hiroshima Math. J. 47(2): 139-153, 2017. https://doi.org/10.32917/hmj/1499392823), De Masi-De Philippis (https://doi.org/10.48550/arXiv.2111.09913), weak capillary surfaces are formulated, using the language of varifolds, and named ”pair of varifolds with fixed contact angle condition”.\n\nIn this talk, we will discuss some recent development in this direction, and prove a strong boundary maximum principle for a specific class of pairs of varifolds with fixed contact angle, which generalizes Li-Zhou’s boundary maximum principle for free boundary varifolds (Comm.\nAnal. Geom. (29): 1509–1521, 2021. https://doi.org/10.4310/CAG.2021.v29.n6.a7). The similar results in the context of rectifiable cones will be discussed as well. If time permits, we will also discuss some applications of the weak formulation, including the establishment of the\nSimon-type monotonicity identities as well as the Li-Yau-type inequalities.
Prescription of Dirac Eigenvalues, Partial Eigenbundles and Surgery
Montag, 11.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The prescription of eigenvalues of the Dirac operator on a closed spin manifold requires, besides the usual analytical methods à la Uhlenbeck and Dahl, also surgery methods to transport spectral data along a bordism. In this talk, I will give the necessary basics as well as an overview of the prescription of double eigenvalues on spin manifolds.
Continuum Limit of Nearest Neighbor and Random Long-Range Interactions
Dienstag, 12.12.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The thesis deals with the limit behavior of discrete energies with different types of interactions between points. On the one hand, only nearest neighbor interactions are considered and on the other hand random long-range interactions. For the latter some assumptions on the conductance have to be made. In a last step, we will try to combine these two types of interactions and investigate whether some assumptions can be dropped in this case.\n\n \n\n
Forcings With the Approximation Property
Dienstag, 12.12.23, 14:30-15:30, Raum 232 in der Stochastik
We introduce the approximation property which was implicit in early work of Mitchell and later defined explicitly by Hamkins. In modern set theory, the approximation property has gotten new attention through the ineffable slender list property (ISP), introduced by Weiss in his PhD thesis. In this talk, we give a criterion for the approximation property which is very applicable to variants of Mitchell Forcing, allowing us to obtain several consistency results regarding ISP.
talks about his Master Thesis
Mittwoch, 13.12.23, 16:00-17:00, Raum 226, Hermann-Herder-Str. 10
Arithmetic aspects of quantum cohomology
Freitag, 15.12.23, 10:30-11:30, Raum 404, Ernst-Zermelo-Str. 1
Shintanis (wenig bekannte) Vermutung zum 12. Hilbertschen Problem besagt, dass abelsche Erweiterungen von \nZahlkörpern mit Hilfe spezieller Werte von verallgemeinerten Gammafunktionen erzeugt werden können.\n\nDiese Vermutung ist seit gut 50 Jahren ungelöst und weitestgehend unverstanden. Unser Vortrag wird daran leider nichts ändern.\n\nEine Hauptschwierigkeit der Shintanischen Vermutung liegt darin, dass (verallgemeinerte) Gammafunktionen sehr schwer handhabbar sind.\n\nIn unserem (elementar gehaltenen) Vortrag wollen wir erklären, wie der Formalismus der Quantumkohomologie neue Einsichten in das Wesen der Gammafunktionen\nliefern könnte.
String Topology of Compact Symmetric Spaces
Montag, 18.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
On the homology of the free loop space of a closed manifold M there exists the so-called Chas-Sullivan product. It is a product defined via the concatenation of loops and can, for example, be used to study closed geodesics of Riemannian or Finsler metrics on M. In this talk I will outline how one can use the geometry of symmetric spaces to partially compute the Chas-Sullivan product. In particular, we will see that the powers of certain non-nilpotent homology classes correspond to the iteration of closed geodesics in a symmetric metric. Some triviality results on the Goresky-Hingston cohomology product will also be mentioned. This talk is based on joint work with Maximilian Stegemeyer.
On strong approximation of SDEs with a discontinuous drift coecient
Dienstag, 19.12.23, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The classical assumption in the literature on numerical approximation of stochastic differential equations (SDEs) is global Lipschitz continuity of the coecients of the equation.\nHowever, many SDEs arising in applications fail to have globally Lipschitz continuous coecients.\nIn the last decade an intensive study of numerical approximation of SDEs with nonglobally Lipschitz continuous coecients has begun. In particular, strong approximation\nof SDEs with a drift coecient that is discontinuous in space has recently gained a lot of\ninterest. Such SDEs arise e.g. in mathematical finance, insurance and stochastic control\nproblems. Classical techniques of error analysis are not applicable to such SDEs and well\nknown convergence results for standard methods do not carry over in general.\n\nIn this talk I will present recent results on strong approximation of such SDEs.\n\nThe talk is based on joint work with Thomas M¨uller-Gronbach (University of Passau).
IP-Mengen, Produktmengen und stabile Formeln
Dienstag, 19.12.23, 14:30-15:30, Raum 404, Ernst-Zermelo-Str. 1
Präsentation der Masterarbeit.